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Improved Lower Bounds on the Reliability of Hypercube Architectures
April 1994 (vol. 5 no. 4)
pp. 364-378

The hypercube topology, also known as the Boolean n-cube, has recently been used for multiprocessing systems. The paper considers two structural-reliability models, namely, terminal reliability (TR) and network reliability (NR), for the hypercube. Terminal (network) reliability is defined as the probability that there exists a working path connecting two (all) nodes. There are no known polynomial time algorithms for exact computation of TR or NR for the hypercube. Thus, lower-bound computation is a better alternative, because it is more efficient computationally, and the system will be at least as reliable as the bound. The paper presents algorithms to compute lower bounds on TR and NR for the hypercube considering node and/or link failures. These algorithms provide tighter bounds for both TR and NR than known results and run in time polynomial in the cube dimension n, specifically, within time O(n/sup 2/).

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Index Terms:
Index Termshypercube networks; parallel architectures; fault tolerant computing; reliability; computational complexity; hypercube topology; Boolean n-cube; lower bounds; reliability; terminal reliability; network reliability; structural-reliability models; hypercube; tighter bounds; time O(n/sup 2/); hypercube architecture; node failure; path generation; reliability bounds; spanning trees
S. Soh, S. Rai, J.L. Trahan, "Improved Lower Bounds on the Reliability of Hypercube Architectures," IEEE Transactions on Parallel and Distributed Systems, vol. 5, no. 4, pp. 364-378, April 1994, doi:10.1109/71.273045
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